Scotland Yard announced yesterday it has set up a special squad to investigate Islamic extremists who demonstrated outside the Danish embassy in London last week, promising a "swift" inquiry which could result in charges of inciting violence or murder.

The announcement came as the government condemned the "completely unacceptable" behaviour of protesters carrying threatening placards and called on the Tories to drop their opposition to a new offence of glorifying terrorism when the terrorism bill returns to the Commons next week.

At least four people have died amid violent street protests around the world against the publication in a Danish newspaper of cartoons satirising the prophet Muhammad.

Yesterday the prime minister's official spokesman said: "We understand the offence caused by the cartoons depicting the prophet and of course regret that this has happened. Such things help no one.

"But nothing can justify the violence aimed at European embassies or at the country of Denmark. We and our EU partners stand in full solidarity with them in resisting this violence and believe the Danish government has done everything it reasonably can to handle a very difficult situation."

He described the behaviour of some demonstrators in London - some of whom held placards threatening a repeat of the September 11 and July 7 attacks, and calling for the beheading of those who insulted Islam - as "completely unacceptable". But he stressed that it was for the police and the Crown Prosecution Service to decide whether further action was justified.

Yesterday a Scotland Yard spokesman said a special team had been set up to investigate the incidents. The police have been criticised since the weekend for not arresting protesters on the spot. He added: "The remit of this team is to review evidence gathered by specialist officers, including police video and sound recording, CCTV and officers' written records.

"Where potential offences have been committed, we will pass evidence to the CPS and we will then take action following their advice and identify offenders who have committed crimes."

Charles Clarke, the home secretary, told the Commons that more powers were needed to combat such behaviour. In an urgent statement, made at the request of the Labour backbencher David Winnick, he urged the Tories to "think long and hard" and support the proposed new glorification offence, which was thrown out by the Lords. But David Cameron, the Tory leader, said: "Many of those people carrying the placards were clearly inciting violence or inciting hatred. That is against the law; it does not need a glorification clause."

Earlier, the Northern Ireland secretary, Peter Hain, told BBC Radio 4's Today programme that the police should "bear down ... very heavily" on protesters acting in an "intolerable" way and prosecute them if there was evidence they had committed offences.

MPs praised the many Muslim organisations that have condemned the demonstration, including the radical Hizb-ut-Tahrir, which the government is seeking to outlaw because of claims it backs terrorism.

One of the most controversial protesters - Omar Khayam, 22, who attended dressed as a suicide bomber - apologised for his "wrong, unjustified and insensitive" behaviour yesterday.

European commission president, José Manuel Barroso, was holding talks with EU governments in an attempt to win "a return to peaceful debate". But his spokesman denied there was any suggestion "at the moment" of reducing or halting aid to countries in which national and EU buildings were targeted.